• Corpus ID: 244773631

Perturbative and non-perturbative effects in ultraperipheral production of lepton pairs

@inproceedings{Dremin2021PerturbativeAN,
  title={Perturbative and non-perturbative effects in ultraperipheral production of lepton pairs},
  author={I. M. Dremin},
  year={2021}
}

• I. Dremin
• Published 1 December 2021
• Physics

Perturbative and non-perturbative terms of the cross sections of ultraperipheral production of lepton pairs in ion collisions are taken into account. It is shown that production of low-mass e+e− pairs is strongly enhanced (compared to perturbative estimates) due to the non-perturbative Sommerfeld-Gamow-Sakharov (SGS) factor. Coulomb attraction of the non-relativistic components of those pairs leads to the finite value of their mass distribution at lowest relative velocities. Their annihilation can result in the increased intensity of 511 keV photons. It can be recorded at the NICA collider and is especially crucial in astrophysical implications regarding the 511 keV line emitted from the Galactic center. The analogous effect can be observed in lepton pairs production at LHC. Energy spectra of lepton pairs created in ultraperipheral nuclear collisions and their transverse momenta are calculated. PACS: 25.75.-q, 34.50.-s, 12.20.-m, 95.30.Cq Interaction of two photons from electromagnetic fields of colliding ions can lead to production of lepton pairs. They are produced in grazing ultraperipheral collisions. This process was first treated perturbatively by Landau and Lifshitz in 1934 [1]. It was shown that its total cross section rapidly increases with increasing energy E as lnE in asymptotics. This is still the strongest asymptotical energy dependence known in particle physics. Moreover, the numerical factor Zα in the total cross section compensates the effect of the small electromagnetic coupling α for heavy ions with large charge Ze. Therefore, the ultraperipheral production of e+e−-pairs (as well as μ+μ− etc) in ion collisions can become the dominant mechanism at very high energies. It is already widely studied at colliders. The heuristic knowledge [e-mail] 1 ar X iv :2 11 2. 00 35 8v 1 [ he pph ] 1 D ec 2 02 1 of these processes is helpful in understanding some important astrophysical phenomena as well. Even earlier, almost a century ago, in 1924, Fermi [2, 3] considered the general problem of interaction of charged objects with matter: ”Let’s calculate, first of all, the spectral distributions corresponding to those of the electric field created by a particle with electric charge, e, passing with velocity, v, at a minimum distance, b, from a point, P .” Fermi obtained the formula for the intensity of the electromagnetic field created by a moving charged object. It was used in 1934 by Weizsäcker [4] and Williams [5] for their formulation of the method of equivalent photons widely applied nowadays for treatment of the ultraperipheral interactions. Solutions of Maxwell equations for the electromagnetic fields of the moving charge are used to derive the Poynting vector. The component of the Poynting vector along the direction of colliding electromagnetic charges defines the total energy of equivalent photons and their energy distribution. The distribution of equivalent photons with a fraction of the nucleon energy x generated by a moving nucleus with the charge Ze can be obtained from the expression for the Poynting vector as dn dx = 2Zα πx ln u(Z) x (1) if integrated over the transverse momentum of scattered nuclei up to some value (see, e.g., Ref. [6]). The physical meaning of the ultraperipherality parameter u(Z) is the ratio of the maximum adoptable transverse momentum to the nucleon mass as the only massless parameter of the problem. Its value is determined by the form factors of colliding ions responsible for their entity (see, e.g., [7]). It is clearly seen from Eq. (1) that soft photons with small fractions x of the nucleon energy dominate in these fluxes. Pairs of leptons with opposite charges are produced in grazing collisions of interacting ions where two photons from their electromagnetic clouds interact. Abundant creation of pairs with rather low pair-masses is the typical feature of ultraperipheral interactions [8]. Two-photon fusion production of lepton pairs has been calculated with both the equivalent photon approximation proposed in [4, 5] and via full lowest-order QED calculations [1, 9, 10, 11, 12] reviewed recently in [13]. According to the equivalent photon approximation, the general expression for the total cross section looks like σup(X) = ∫ dx1dx2 dn dx1 dn dx2 σγγ(X). (2)